Properties

Label 342.2.s.a.107.1
Level $342$
Weight $2$
Character 342.107
Analytic conductor $2.731$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.73088374913\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 342.107
Dual form 342.2.s.a.179.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +(1.22474 + 0.707107i) q^{10} -0.635674i q^{11} +(5.17423 + 2.98735i) q^{13} +(-0.724745 - 1.25529i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.77526 - 1.02494i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.41421i q^{20} +(-0.550510 + 0.317837i) q^{22} +(4.89898 + 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.97469i q^{26} +(-0.724745 + 1.25529i) q^{28} +(1.22474 - 2.12132i) q^{29} -0.953512i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.77526 - 1.02494i) q^{34} +(-1.77526 + 1.02494i) q^{35} -2.51059i q^{37} +(-3.50000 - 2.59808i) q^{38} +(-1.22474 + 0.707107i) q^{40} +(-1.94949 - 3.37662i) q^{43} +(0.550510 + 0.317837i) q^{44} -5.65685i q^{46} +(-1.77526 - 1.02494i) q^{47} -4.89898 q^{49} +3.00000 q^{50} +(-5.17423 + 2.98735i) q^{52} +(-2.44949 + 4.24264i) q^{53} +(0.449490 + 0.778539i) q^{55} +1.44949 q^{56} -2.44949 q^{58} +(7.22474 + 12.5136i) q^{59} +(1.72474 - 2.98735i) q^{61} +(-0.825765 + 0.476756i) q^{62} +1.00000 q^{64} -8.44949 q^{65} +(-8.84847 - 5.10867i) q^{67} +2.04989i q^{68} +(1.77526 + 1.02494i) q^{70} +(3.00000 + 5.19615i) q^{71} +(1.05051 + 1.81954i) q^{73} +(-2.17423 + 1.25529i) q^{74} +(-0.500000 + 4.33013i) q^{76} -0.921404i q^{77} +(0.825765 - 0.476756i) q^{79} +(1.22474 + 0.707107i) q^{80} -11.8065i q^{83} +(-1.44949 + 2.51059i) q^{85} +(-1.94949 + 3.37662i) q^{86} -0.635674i q^{88} +(-6.12372 + 10.6066i) q^{89} +(7.50000 + 4.33013i) q^{91} +(-4.89898 + 2.82843i) q^{92} +2.04989i q^{94} +(-3.67423 + 4.94975i) q^{95} +(-16.3485 + 9.43879i) q^{97} +(2.44949 + 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} - 4q^{7} + 4q^{8} + 6q^{13} + 2q^{14} - 2q^{16} + 12q^{17} + 16q^{19} - 12q^{22} - 6q^{25} + 2q^{28} - 2q^{32} - 12q^{34} - 12q^{35} - 14q^{38} + 2q^{43} + 12q^{44} - 12q^{47} + 12q^{50} - 6q^{52} - 8q^{55} - 4q^{56} + 24q^{59} + 2q^{61} - 18q^{62} + 4q^{64} - 24q^{65} - 6q^{67} + 12q^{70} + 12q^{71} + 14q^{73} + 6q^{74} - 2q^{76} + 18q^{79} + 4q^{85} + 2q^{86} + 30q^{91} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.22474 + 0.707107i −0.547723 + 0.316228i −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 0 0
\(7\) 1.44949 0.547856 0.273928 0.961750i \(-0.411677\pi\)
0.273928 + 0.961750i \(0.411677\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.22474 + 0.707107i 0.387298 + 0.223607i
\(11\) 0.635674i 0.191663i −0.995398 0.0958315i \(-0.969449\pi\)
0.995398 0.0958315i \(-0.0305510\pi\)
\(12\) 0 0
\(13\) 5.17423 + 2.98735i 1.43507 + 0.828541i 0.997502 0.0706424i \(-0.0225049\pi\)
0.437573 + 0.899183i \(0.355838\pi\)
\(14\) −0.724745 1.25529i −0.193696 0.335492i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.77526 1.02494i 0.430563 0.248585i −0.269024 0.963134i \(-0.586701\pi\)
0.699586 + 0.714548i \(0.253368\pi\)
\(18\) 0 0
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) 1.41421i 0.316228i
\(21\) 0 0
\(22\) −0.550510 + 0.317837i −0.117369 + 0.0677631i
\(23\) 4.89898 + 2.82843i 1.02151 + 0.589768i 0.914540 0.404495i \(-0.132553\pi\)
0.106967 + 0.994263i \(0.465886\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 5.97469i 1.17173i
\(27\) 0 0
\(28\) −0.724745 + 1.25529i −0.136964 + 0.237228i
\(29\) 1.22474 2.12132i 0.227429 0.393919i −0.729616 0.683857i \(-0.760301\pi\)
0.957046 + 0.289938i \(0.0936346\pi\)
\(30\) 0 0
\(31\) 0.953512i 0.171256i −0.996327 0.0856279i \(-0.972710\pi\)
0.996327 0.0856279i \(-0.0272896\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.77526 1.02494i −0.304454 0.175776i
\(35\) −1.77526 + 1.02494i −0.300073 + 0.173247i
\(36\) 0 0
\(37\) 2.51059i 0.412738i −0.978474 0.206369i \(-0.933835\pi\)
0.978474 0.206369i \(-0.0661648\pi\)
\(38\) −3.50000 2.59808i −0.567775 0.421464i
\(39\) 0 0
\(40\) −1.22474 + 0.707107i −0.193649 + 0.111803i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) −1.94949 3.37662i −0.297294 0.514929i 0.678222 0.734857i \(-0.262751\pi\)
−0.975516 + 0.219928i \(0.929418\pi\)
\(44\) 0.550510 + 0.317837i 0.0829925 + 0.0479158i
\(45\) 0 0
\(46\) 5.65685i 0.834058i
\(47\) −1.77526 1.02494i −0.258948 0.149503i 0.364907 0.931044i \(-0.381101\pi\)
−0.623854 + 0.781541i \(0.714434\pi\)
\(48\) 0 0
\(49\) −4.89898 −0.699854
\(50\) 3.00000 0.424264
\(51\) 0 0
\(52\) −5.17423 + 2.98735i −0.717537 + 0.414270i
\(53\) −2.44949 + 4.24264i −0.336463 + 0.582772i −0.983765 0.179463i \(-0.942564\pi\)
0.647302 + 0.762234i \(0.275897\pi\)
\(54\) 0 0
\(55\) 0.449490 + 0.778539i 0.0606092 + 0.104978i
\(56\) 1.44949 0.193696
\(57\) 0 0
\(58\) −2.44949 −0.321634
\(59\) 7.22474 + 12.5136i 0.940582 + 1.62914i 0.764365 + 0.644784i \(0.223053\pi\)
0.176217 + 0.984351i \(0.443614\pi\)
\(60\) 0 0
\(61\) 1.72474 2.98735i 0.220831 0.382490i −0.734230 0.678901i \(-0.762456\pi\)
0.955061 + 0.296411i \(0.0957898\pi\)
\(62\) −0.825765 + 0.476756i −0.104872 + 0.0605481i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.44949 −1.04803
\(66\) 0 0
\(67\) −8.84847 5.10867i −1.08101 0.624123i −0.149843 0.988710i \(-0.547877\pi\)
−0.931169 + 0.364587i \(0.881210\pi\)
\(68\) 2.04989i 0.248585i
\(69\) 0 0
\(70\) 1.77526 + 1.02494i 0.212184 + 0.122504i
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 1.05051 + 1.81954i 0.122953 + 0.212961i 0.920931 0.389726i \(-0.127430\pi\)
−0.797978 + 0.602687i \(0.794097\pi\)
\(74\) −2.17423 + 1.25529i −0.252750 + 0.145925i
\(75\) 0 0
\(76\) −0.500000 + 4.33013i −0.0573539 + 0.496700i
\(77\) 0.921404i 0.105004i
\(78\) 0 0
\(79\) 0.825765 0.476756i 0.0929059 0.0536392i −0.452827 0.891598i \(-0.649585\pi\)
0.545733 + 0.837959i \(0.316251\pi\)
\(80\) 1.22474 + 0.707107i 0.136931 + 0.0790569i
\(81\) 0 0
\(82\) 0 0
\(83\) 11.8065i 1.29593i −0.761669 0.647967i \(-0.775620\pi\)
0.761669 0.647967i \(-0.224380\pi\)
\(84\) 0 0
\(85\) −1.44949 + 2.51059i −0.157219 + 0.272312i
\(86\) −1.94949 + 3.37662i −0.210219 + 0.364110i
\(87\) 0 0
\(88\) 0.635674i 0.0677631i
\(89\) −6.12372 + 10.6066i −0.649113 + 1.12430i 0.334221 + 0.942495i \(0.391527\pi\)
−0.983335 + 0.181803i \(0.941807\pi\)
\(90\) 0 0
\(91\) 7.50000 + 4.33013i 0.786214 + 0.453921i
\(92\) −4.89898 + 2.82843i −0.510754 + 0.294884i
\(93\) 0 0
\(94\) 2.04989i 0.211430i
\(95\) −3.67423 + 4.94975i −0.376969 + 0.507833i
\(96\) 0 0
\(97\) −16.3485 + 9.43879i −1.65994 + 0.958364i −0.687193 + 0.726474i \(0.741158\pi\)
−0.972742 + 0.231890i \(0.925509\pi\)
\(98\) 2.44949 + 4.24264i 0.247436 + 0.428571i
\(99\) 0 0
\(100\) −1.50000 2.59808i −0.150000 0.259808i
\(101\) −11.4495 6.61037i −1.13927 0.657756i −0.193018 0.981195i \(-0.561828\pi\)
−0.946249 + 0.323439i \(0.895161\pi\)
\(102\) 0 0
\(103\) 14.4600i 1.42478i −0.701782 0.712392i \(-0.747612\pi\)
0.701782 0.712392i \(-0.252388\pi\)
\(104\) 5.17423 + 2.98735i 0.507375 + 0.292933i
\(105\) 0 0
\(106\) 4.89898 0.475831
\(107\) 15.7980 1.52725 0.763623 0.645662i \(-0.223419\pi\)
0.763623 + 0.645662i \(0.223419\pi\)
\(108\) 0 0
\(109\) −14.6969 + 8.48528i −1.40771 + 0.812743i −0.995167 0.0981950i \(-0.968693\pi\)
−0.412544 + 0.910938i \(0.635360\pi\)
\(110\) 0.449490 0.778539i 0.0428572 0.0742308i
\(111\) 0 0
\(112\) −0.724745 1.25529i −0.0684820 0.118614i
\(113\) −17.1464 −1.61300 −0.806500 0.591234i \(-0.798641\pi\)
−0.806500 + 0.591234i \(0.798641\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) 1.22474 + 2.12132i 0.113715 + 0.196960i
\(117\) 0 0
\(118\) 7.22474 12.5136i 0.665092 1.15197i
\(119\) 2.57321 1.48565i 0.235886 0.136189i
\(120\) 0 0
\(121\) 10.5959 0.963265
\(122\) −3.44949 −0.312302
\(123\) 0 0
\(124\) 0.825765 + 0.476756i 0.0741559 + 0.0428139i
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) 7.34847 + 4.24264i 0.652071 + 0.376473i 0.789249 0.614073i \(-0.210470\pi\)
−0.137178 + 0.990546i \(0.543803\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 4.22474 + 7.31747i 0.370535 + 0.641785i
\(131\) 12.7980 7.38891i 1.11816 0.645572i 0.177232 0.984169i \(-0.443286\pi\)
0.940931 + 0.338598i \(0.109953\pi\)
\(132\) 0 0
\(133\) 5.79796 2.51059i 0.502747 0.217696i
\(134\) 10.2173i 0.882643i
\(135\) 0 0
\(136\) 1.77526 1.02494i 0.152227 0.0878882i
\(137\) −5.44949 3.14626i −0.465581 0.268804i 0.248807 0.968553i \(-0.419962\pi\)
−0.714388 + 0.699750i \(0.753295\pi\)
\(138\) 0 0
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 2.04989i 0.173247i
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 1.89898 3.28913i 0.158801 0.275051i
\(144\) 0 0
\(145\) 3.46410i 0.287678i
\(146\) 1.05051 1.81954i 0.0869408 0.150586i
\(147\) 0 0
\(148\) 2.17423 + 1.25529i 0.178721 + 0.103185i
\(149\) 17.4495 10.0745i 1.42952 0.825333i 0.432435 0.901665i \(-0.357654\pi\)
0.997082 + 0.0763323i \(0.0243210\pi\)
\(150\) 0 0
\(151\) 1.55708i 0.126713i −0.997991 0.0633566i \(-0.979819\pi\)
0.997991 0.0633566i \(-0.0201806\pi\)
\(152\) 4.00000 1.73205i 0.324443 0.140488i
\(153\) 0 0
\(154\) −0.797959 + 0.460702i −0.0643014 + 0.0371244i
\(155\) 0.674235 + 1.16781i 0.0541558 + 0.0938006i
\(156\) 0 0
\(157\) −6.17423 10.6941i −0.492758 0.853481i 0.507208 0.861824i \(-0.330678\pi\)
−0.999965 + 0.00834275i \(0.997344\pi\)
\(158\) −0.825765 0.476756i −0.0656944 0.0379287i
\(159\) 0 0
\(160\) 1.41421i 0.111803i
\(161\) 7.10102 + 4.09978i 0.559639 + 0.323108i
\(162\) 0 0
\(163\) 7.69694 0.602871 0.301435 0.953487i \(-0.402534\pi\)
0.301435 + 0.953487i \(0.402534\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −10.2247 + 5.90326i −0.793594 + 0.458182i
\(167\) 4.22474 7.31747i 0.326921 0.566243i −0.654979 0.755647i \(-0.727322\pi\)
0.981899 + 0.189404i \(0.0606557\pi\)
\(168\) 0 0
\(169\) 11.3485 + 19.6561i 0.872959 + 1.51201i
\(170\) 2.89898 0.222342
\(171\) 0 0
\(172\) 3.89898 0.297294
\(173\) −6.12372 10.6066i −0.465578 0.806405i 0.533649 0.845706i \(-0.320820\pi\)
−0.999227 + 0.0393009i \(0.987487\pi\)
\(174\) 0 0
\(175\) −2.17423 + 3.76588i −0.164357 + 0.284674i
\(176\) −0.550510 + 0.317837i −0.0414963 + 0.0239579i
\(177\) 0 0
\(178\) 12.2474 0.917985
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −4.65153 2.68556i −0.345746 0.199616i 0.317064 0.948404i \(-0.397303\pi\)
−0.662810 + 0.748788i \(0.730636\pi\)
\(182\) 8.66025i 0.641941i
\(183\) 0 0
\(184\) 4.89898 + 2.82843i 0.361158 + 0.208514i
\(185\) 1.77526 + 3.07483i 0.130519 + 0.226066i
\(186\) 0 0
\(187\) −0.651531 1.12848i −0.0476446 0.0825230i
\(188\) 1.77526 1.02494i 0.129474 0.0747517i
\(189\) 0 0
\(190\) 6.12372 + 0.707107i 0.444262 + 0.0512989i
\(191\) 15.2706i 1.10494i −0.833532 0.552472i \(-0.813685\pi\)
0.833532 0.552472i \(-0.186315\pi\)
\(192\) 0 0
\(193\) 14.8485 8.57277i 1.06882 0.617081i 0.140958 0.990016i \(-0.454982\pi\)
0.927858 + 0.372934i \(0.121648\pi\)
\(194\) 16.3485 + 9.43879i 1.17375 + 0.677666i
\(195\) 0 0
\(196\) 2.44949 4.24264i 0.174964 0.303046i
\(197\) 20.2918i 1.44573i −0.690989 0.722865i \(-0.742825\pi\)
0.690989 0.722865i \(-0.257175\pi\)
\(198\) 0 0
\(199\) −8.62372 + 14.9367i −0.611320 + 1.05884i 0.379699 + 0.925110i \(0.376028\pi\)
−0.991018 + 0.133726i \(0.957306\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) 13.2207i 0.930207i
\(203\) 1.77526 3.07483i 0.124598 0.215811i
\(204\) 0 0
\(205\) 0 0
\(206\) −12.5227 + 7.22999i −0.872498 + 0.503737i
\(207\) 0 0
\(208\) 5.97469i 0.414270i
\(209\) −1.10102 2.54270i −0.0761592 0.175882i
\(210\) 0 0
\(211\) 3.15153 1.81954i 0.216960 0.125262i −0.387582 0.921835i \(-0.626689\pi\)
0.604542 + 0.796573i \(0.293356\pi\)
\(212\) −2.44949 4.24264i −0.168232 0.291386i
\(213\) 0 0
\(214\) −7.89898 13.6814i −0.539963 0.935244i
\(215\) 4.77526 + 2.75699i 0.325670 + 0.188025i
\(216\) 0 0
\(217\) 1.38211i 0.0938234i
\(218\) 14.6969 + 8.48528i 0.995402 + 0.574696i
\(219\) 0 0
\(220\) −0.898979 −0.0606092
\(221\) 12.2474 0.823853
\(222\) 0 0
\(223\) −2.17423 + 1.25529i −0.145598 + 0.0840608i −0.571029 0.820930i \(-0.693456\pi\)
0.425432 + 0.904991i \(0.360122\pi\)
\(224\) −0.724745 + 1.25529i −0.0484241 + 0.0838729i
\(225\) 0 0
\(226\) 8.57321 + 14.8492i 0.570282 + 0.987757i
\(227\) −23.1464 −1.53628 −0.768141 0.640280i \(-0.778818\pi\)
−0.768141 + 0.640280i \(0.778818\pi\)
\(228\) 0 0
\(229\) −19.2474 −1.27191 −0.635954 0.771727i \(-0.719393\pi\)
−0.635954 + 0.771727i \(0.719393\pi\)
\(230\) 4.00000 + 6.92820i 0.263752 + 0.456832i
\(231\) 0 0
\(232\) 1.22474 2.12132i 0.0804084 0.139272i
\(233\) −15.2474 + 8.80312i −0.998894 + 0.576711i −0.907921 0.419142i \(-0.862331\pi\)
−0.0909728 + 0.995853i \(0.528998\pi\)
\(234\) 0 0
\(235\) 2.89898 0.189109
\(236\) −14.4495 −0.940582
\(237\) 0 0
\(238\) −2.57321 1.48565i −0.166797 0.0963001i
\(239\) 22.4846i 1.45440i 0.686423 + 0.727202i \(0.259180\pi\)
−0.686423 + 0.727202i \(0.740820\pi\)
\(240\) 0 0
\(241\) 12.1515 + 7.01569i 0.782749 + 0.451920i 0.837404 0.546585i \(-0.184072\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) −5.29796 9.17633i −0.340566 0.589877i
\(243\) 0 0
\(244\) 1.72474 + 2.98735i 0.110415 + 0.191245i
\(245\) 6.00000 3.46410i 0.383326 0.221313i
\(246\) 0 0
\(247\) 25.8712 + 2.98735i 1.64614 + 0.190080i
\(248\) 0.953512i 0.0605481i
\(249\) 0 0
\(250\) −9.79796 + 5.65685i −0.619677 + 0.357771i
\(251\) 1.22474 + 0.707107i 0.0773052 + 0.0446322i 0.538154 0.842846i \(-0.319122\pi\)
−0.460849 + 0.887478i \(0.652455\pi\)
\(252\) 0 0
\(253\) 1.79796 3.11416i 0.113037 0.195785i
\(254\) 8.48528i 0.532414i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i \(-0.955440\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(258\) 0 0
\(259\) 3.63907i 0.226121i
\(260\) 4.22474 7.31747i 0.262008 0.453810i
\(261\) 0 0
\(262\) −12.7980 7.38891i −0.790661 0.456488i
\(263\) 0.797959 0.460702i 0.0492043 0.0284081i −0.475196 0.879880i \(-0.657623\pi\)
0.524400 + 0.851472i \(0.324290\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) −5.07321 3.76588i −0.311059 0.230901i
\(267\) 0 0
\(268\) 8.84847 5.10867i 0.540506 0.312061i
\(269\) 10.2247 + 17.7098i 0.623414 + 1.07978i 0.988845 + 0.148946i \(0.0475881\pi\)
−0.365432 + 0.930838i \(0.619079\pi\)
\(270\) 0 0
\(271\) −15.6969 27.1879i −0.953521 1.65155i −0.737717 0.675110i \(-0.764096\pi\)
−0.215804 0.976437i \(-0.569237\pi\)
\(272\) −1.77526 1.02494i −0.107641 0.0621464i
\(273\) 0 0
\(274\) 6.29253i 0.380146i
\(275\) 1.65153 + 0.953512i 0.0995911 + 0.0574989i
\(276\) 0 0
\(277\) 9.10102 0.546827 0.273414 0.961897i \(-0.411847\pi\)
0.273414 + 0.961897i \(0.411847\pi\)
\(278\) −7.00000 −0.419832
\(279\) 0 0
\(280\) −1.77526 + 1.02494i −0.106092 + 0.0612521i
\(281\) −11.5732 + 20.0454i −0.690400 + 1.19581i 0.281307 + 0.959618i \(0.409232\pi\)
−0.971707 + 0.236190i \(0.924101\pi\)
\(282\) 0 0
\(283\) 7.44949 + 12.9029i 0.442826 + 0.766997i 0.997898 0.0648050i \(-0.0206425\pi\)
−0.555072 + 0.831802i \(0.687309\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) −3.79796 −0.224578
\(287\) 0 0
\(288\) 0 0
\(289\) −6.39898 + 11.0834i −0.376411 + 0.651962i
\(290\) 3.00000 1.73205i 0.176166 0.101710i
\(291\) 0 0
\(292\) −2.10102 −0.122953
\(293\) −10.6515 −0.622269 −0.311135 0.950366i \(-0.600709\pi\)
−0.311135 + 0.950366i \(0.600709\pi\)
\(294\) 0 0
\(295\) −17.6969 10.2173i −1.03036 0.594876i
\(296\) 2.51059i 0.145925i
\(297\) 0 0
\(298\) −17.4495 10.0745i −1.01082 0.583598i
\(299\) 16.8990 + 29.2699i 0.977293 + 1.69272i
\(300\) 0 0
\(301\) −2.82577 4.89437i −0.162874 0.282107i
\(302\) −1.34847 + 0.778539i −0.0775957 + 0.0447999i
\(303\) 0 0
\(304\) −3.50000 2.59808i −0.200739 0.149010i
\(305\) 4.87832i 0.279332i
\(306\) 0 0
\(307\) −13.3485 + 7.70674i −0.761837 + 0.439847i −0.829955 0.557830i \(-0.811634\pi\)
0.0681177 + 0.997677i \(0.478301\pi\)
\(308\) 0.797959 + 0.460702i 0.0454679 + 0.0262509i
\(309\) 0 0
\(310\) 0.674235 1.16781i 0.0382940 0.0663271i
\(311\) 5.16404i 0.292826i 0.989224 + 0.146413i \(0.0467729\pi\)
−0.989224 + 0.146413i \(0.953227\pi\)
\(312\) 0 0
\(313\) −11.3485 + 19.6561i −0.641453 + 1.11103i 0.343655 + 0.939096i \(0.388335\pi\)
−0.985108 + 0.171934i \(0.944998\pi\)
\(314\) −6.17423 + 10.6941i −0.348432 + 0.603502i
\(315\) 0 0
\(316\) 0.953512i 0.0536392i
\(317\) 3.67423 6.36396i 0.206366 0.357436i −0.744201 0.667955i \(-0.767170\pi\)
0.950567 + 0.310520i \(0.100503\pi\)
\(318\) 0 0
\(319\) −1.34847 0.778539i −0.0754998 0.0435898i
\(320\) −1.22474 + 0.707107i −0.0684653 + 0.0395285i
\(321\) 0 0
\(322\) 8.19955i 0.456943i
\(323\) 5.32577 7.17461i 0.296334 0.399206i
\(324\) 0 0
\(325\) −15.5227 + 8.96204i −0.861045 + 0.497124i
\(326\) −3.84847 6.66574i −0.213147 0.369181i
\(327\) 0 0
\(328\) 0 0
\(329\) −2.57321 1.48565i −0.141866 0.0819063i
\(330\) 0 0
\(331\) 18.7026i 1.02799i −0.857794 0.513994i \(-0.828165\pi\)
0.857794 0.513994i \(-0.171835\pi\)
\(332\) 10.2247 + 5.90326i 0.561156 + 0.323983i
\(333\) 0 0
\(334\) −8.44949 −0.462336
\(335\) 14.4495 0.789460
\(336\) 0 0
\(337\) 1.80306 1.04100i 0.0982190 0.0567068i −0.450086 0.892985i \(-0.648607\pi\)
0.548305 + 0.836278i \(0.315273\pi\)
\(338\) 11.3485 19.6561i 0.617275 1.06915i
\(339\) 0 0
\(340\) −1.44949 2.51059i −0.0786096 0.136156i
\(341\) −0.606123 −0.0328234
\(342\) 0 0
\(343\) −17.2474 −0.931275
\(344\) −1.94949 3.37662i −0.105109 0.182055i
\(345\) 0 0
\(346\) −6.12372 + 10.6066i −0.329213 + 0.570214i
\(347\) −28.2247 + 16.2956i −1.51518 + 0.874792i −0.515342 + 0.856984i \(0.672335\pi\)
−0.999841 + 0.0178073i \(0.994331\pi\)
\(348\) 0 0
\(349\) 23.2474 1.24441 0.622204 0.782855i \(-0.286238\pi\)
0.622204 + 0.782855i \(0.286238\pi\)
\(350\) 4.34847 0.232435
\(351\) 0 0
\(352\) 0.550510 + 0.317837i 0.0293423 + 0.0169408i
\(353\) 3.32124i 0.176772i −0.996086 0.0883858i \(-0.971829\pi\)
0.996086 0.0883858i \(-0.0281708\pi\)
\(354\) 0 0
\(355\) −7.34847 4.24264i −0.390016 0.225176i
\(356\) −6.12372 10.6066i −0.324557 0.562149i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 9.79796 5.65685i 0.517116 0.298557i −0.218638 0.975806i \(-0.570161\pi\)
0.735754 + 0.677249i \(0.236828\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 5.37113i 0.282300i
\(363\) 0 0
\(364\) −7.50000 + 4.33013i −0.393107 + 0.226960i
\(365\) −2.57321 1.48565i −0.134688 0.0777623i
\(366\) 0 0
\(367\) 7.17423 12.4261i 0.374492 0.648639i −0.615759 0.787935i \(-0.711150\pi\)
0.990251 + 0.139295i \(0.0444838\pi\)
\(368\) 5.65685i 0.294884i
\(369\) 0 0
\(370\) 1.77526 3.07483i 0.0922911 0.159853i
\(371\) −3.55051 + 6.14966i −0.184333 + 0.319275i
\(372\) 0 0
\(373\) 12.2993i 0.636835i −0.947951 0.318418i \(-0.896849\pi\)
0.947951 0.318418i \(-0.103151\pi\)
\(374\) −0.651531 + 1.12848i −0.0336899 + 0.0583525i
\(375\) 0 0
\(376\) −1.77526 1.02494i −0.0915518 0.0528575i
\(377\) 12.6742 7.31747i 0.652756 0.376869i
\(378\) 0 0
\(379\) 19.0526i 0.978664i 0.872098 + 0.489332i \(0.162759\pi\)
−0.872098 + 0.489332i \(0.837241\pi\)
\(380\) −2.44949 5.65685i −0.125656 0.290191i
\(381\) 0 0
\(382\) −13.2247 + 7.63531i −0.676637 + 0.390656i
\(383\) −5.44949 9.43879i −0.278456 0.482300i 0.692545 0.721374i \(-0.256489\pi\)
−0.971001 + 0.239075i \(0.923156\pi\)
\(384\) 0 0
\(385\) 0.651531 + 1.12848i 0.0332051 + 0.0575129i
\(386\) −14.8485 8.57277i −0.755767 0.436342i
\(387\) 0 0
\(388\) 18.8776i 0.958364i
\(389\) 22.8990 + 13.2207i 1.16102 + 0.670318i 0.951549 0.307496i \(-0.0994912\pi\)
0.209475 + 0.977814i \(0.432824\pi\)
\(390\) 0 0
\(391\) 11.5959 0.586431
\(392\) −4.89898 −0.247436
\(393\) 0 0
\(394\) −17.5732 + 10.1459i −0.885326 + 0.511143i
\(395\) −0.674235 + 1.16781i −0.0339244 + 0.0587588i
\(396\) 0 0
\(397\) −10.8258 18.7508i −0.543330 0.941074i −0.998710 0.0507775i \(-0.983830\pi\)
0.455380 0.890297i \(-0.349503\pi\)
\(398\) 17.2474 0.864536
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 0.123724 + 0.214297i 0.00617850 + 0.0107015i 0.869098 0.494640i \(-0.164700\pi\)
−0.862920 + 0.505341i \(0.831367\pi\)
\(402\) 0 0
\(403\) 2.84847 4.93369i 0.141892 0.245765i
\(404\) 11.4495 6.61037i 0.569633 0.328878i
\(405\) 0 0
\(406\) −3.55051 −0.176209
\(407\) −1.59592 −0.0791067
\(408\) 0 0
\(409\) −25.0454 14.4600i −1.23842 0.715000i −0.269645 0.962960i \(-0.586906\pi\)
−0.968770 + 0.247960i \(0.920240\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 12.5227 + 7.22999i 0.616949 + 0.356196i
\(413\) 10.4722 + 18.1384i 0.515303 + 0.892531i
\(414\) 0 0
\(415\) 8.34847 + 14.4600i 0.409810 + 0.709812i
\(416\) −5.17423 + 2.98735i −0.253688 + 0.146467i
\(417\) 0 0
\(418\) −1.65153 + 2.22486i −0.0807790 + 0.108821i
\(419\) 3.74983i 0.183191i −0.995796 0.0915956i \(-0.970803\pi\)
0.995796 0.0915956i \(-0.0291967\pi\)
\(420\) 0 0
\(421\) 1.34847 0.778539i 0.0657204 0.0379437i −0.466780 0.884374i \(-0.654586\pi\)
0.532500 + 0.846430i \(0.321253\pi\)
\(422\) −3.15153 1.81954i −0.153414 0.0885737i
\(423\) 0 0
\(424\) −2.44949 + 4.24264i −0.118958 + 0.206041i
\(425\) 6.14966i 0.298303i
\(426\) 0 0
\(427\) 2.50000 4.33013i 0.120983 0.209550i
\(428\) −7.89898 + 13.6814i −0.381812 + 0.661317i
\(429\) 0 0
\(430\) 5.51399i 0.265908i
\(431\) −8.02270 + 13.8957i −0.386440 + 0.669334i −0.991968 0.126490i \(-0.959629\pi\)
0.605528 + 0.795824i \(0.292962\pi\)
\(432\) 0 0
\(433\) 25.1969 + 14.5475i 1.21089 + 0.699106i 0.962953 0.269670i \(-0.0869148\pi\)
0.247935 + 0.968777i \(0.420248\pi\)
\(434\) −1.19694 + 0.691053i −0.0574549 + 0.0331716i
\(435\) 0 0
\(436\) 16.9706i 0.812743i
\(437\) 24.4949 + 2.82843i 1.17175 + 0.135302i
\(438\) 0 0
\(439\) −12.5227 + 7.22999i −0.597676 + 0.345068i −0.768127 0.640298i \(-0.778811\pi\)
0.170451 + 0.985366i \(0.445478\pi\)
\(440\) 0.449490 + 0.778539i 0.0214286 + 0.0371154i
\(441\) 0 0
\(442\) −6.12372 10.6066i −0.291276 0.504505i
\(443\) −25.7753 14.8814i −1.22462 0.707034i −0.258720 0.965952i \(-0.583301\pi\)
−0.965899 + 0.258918i \(0.916634\pi\)
\(444\) 0 0
\(445\) 17.3205i 0.821071i
\(446\) 2.17423 + 1.25529i 0.102953 + 0.0594399i
\(447\) 0 0
\(448\) 1.44949 0.0684820
\(449\) −18.2474 −0.861150 −0.430575 0.902555i \(-0.641689\pi\)
−0.430575 + 0.902555i \(0.641689\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 8.57321 14.8492i 0.403250 0.698450i
\(453\) 0 0
\(454\) 11.5732 + 20.0454i 0.543158 + 0.940777i
\(455\) −12.2474 −0.574169
\(456\) 0 0
\(457\) 19.6969 0.921384 0.460692 0.887560i \(-0.347601\pi\)
0.460692 + 0.887560i \(0.347601\pi\)
\(458\) 9.62372 + 16.6688i 0.449687 + 0.778881i
\(459\) 0 0
\(460\) 4.00000 6.92820i 0.186501 0.323029i
\(461\) 9.12372 5.26758i 0.424934 0.245336i −0.272252 0.962226i \(-0.587768\pi\)
0.697186 + 0.716890i \(0.254435\pi\)
\(462\) 0 0
\(463\) 40.1464 1.86576 0.932881 0.360184i \(-0.117286\pi\)
0.932881 + 0.360184i \(0.117286\pi\)
\(464\) −2.44949 −0.113715
\(465\) 0 0
\(466\) 15.2474 + 8.80312i 0.706324 + 0.407797i
\(467\) 21.0703i 0.975019i −0.873118 0.487510i \(-0.837905\pi\)
0.873118 0.487510i \(-0.162095\pi\)
\(468\) 0 0
\(469\) −12.8258 7.40496i −0.592239 0.341929i
\(470\) −1.44949 2.51059i −0.0668600 0.115805i
\(471\) 0 0
\(472\) 7.22474 + 12.5136i 0.332546 + 0.575986i
\(473\) −2.14643 + 1.23924i −0.0986929 + 0.0569804i
\(474\) 0 0
\(475\) −1.50000 + 12.9904i −0.0688247 + 0.596040i
\(476\) 2.97129i 0.136189i
\(477\) 0 0
\(478\) 19.4722 11.2423i 0.890637 0.514210i
\(479\) −8.14643 4.70334i −0.372220 0.214901i 0.302208 0.953242i \(-0.402276\pi\)
−0.674428 + 0.738341i \(0.735610\pi\)
\(480\) 0 0
\(481\) 7.50000 12.9904i 0.341971 0.592310i
\(482\) 14.0314i 0.639112i
\(483\) 0 0
\(484\) −5.29796 + 9.17633i −0.240816 + 0.417106i
\(485\) 13.3485 23.1202i 0.606123 1.04984i
\(486\) 0 0
\(487\) 39.6622i 1.79727i 0.438702 + 0.898633i \(0.355439\pi\)
−0.438702 + 0.898633i \(0.644561\pi\)
\(488\) 1.72474 2.98735i 0.0780755 0.135231i
\(489\) 0 0
\(490\) −6.00000 3.46410i −0.271052 0.156492i
\(491\) 26.1464 15.0956i 1.17997 0.681257i 0.223964 0.974597i \(-0.428100\pi\)
0.956008 + 0.293340i \(0.0947669\pi\)
\(492\) 0 0
\(493\) 5.02118i 0.226143i
\(494\) −10.3485 23.8988i −0.465600 1.07526i
\(495\) 0 0
\(496\) −0.825765 + 0.476756i −0.0370780 + 0.0214070i
\(497\) 4.34847 + 7.53177i 0.195056 + 0.337846i
\(498\) 0 0
\(499\) 21.7474 + 37.6677i 0.973550 + 1.68624i 0.684641 + 0.728881i \(0.259959\pi\)
0.288909 + 0.957357i \(0.406708\pi\)
\(500\) 9.79796 + 5.65685i 0.438178 + 0.252982i
\(501\) 0 0
\(502\) 1.41421i 0.0631194i
\(503\) −35.5176 20.5061i −1.58365 0.914322i −0.994320 0.106430i \(-0.966058\pi\)
−0.589331 0.807891i \(-0.700609\pi\)
\(504\) 0 0
\(505\) 18.6969 0.832003
\(506\) −3.59592 −0.159858
\(507\) 0 0
\(508\) −7.34847 + 4.24264i −0.326036 + 0.188237i
\(509\) −6.67423 + 11.5601i −0.295830 + 0.512393i −0.975178 0.221424i \(-0.928930\pi\)
0.679347 + 0.733817i \(0.262263\pi\)
\(510\) 0 0
\(511\) 1.52270 + 2.63740i 0.0673605 + 0.116672i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) 10.2247 + 17.7098i 0.450556 + 0.780386i
\(516\) 0 0
\(517\) −0.651531 + 1.12848i −0.0286543 + 0.0496307i
\(518\) −3.15153 + 1.81954i −0.138470 + 0.0799459i
\(519\) 0 0
\(520\) −8.44949 −0.370535
\(521\) −8.20204 −0.359338 −0.179669 0.983727i \(-0.557503\pi\)
−0.179669 + 0.983727i \(0.557503\pi\)
\(522\) 0 0
\(523\) 13.5000 + 7.79423i 0.590314 + 0.340818i 0.765222 0.643767i \(-0.222629\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 14.7778i 0.645572i
\(525\) 0 0
\(526\) −0.797959 0.460702i −0.0347927 0.0200876i
\(527\) −0.977296 1.69273i −0.0425717 0.0737363i
\(528\) 0 0
\(529\) 4.50000 + 7.79423i 0.195652 + 0.338880i
\(530\) −6.00000 + 3.46410i −0.260623 + 0.150471i
\(531\) 0 0
\(532\) −0.724745 + 6.27647i −0.0314217 + 0.272120i
\(533\) 0 0
\(534\) 0 0
\(535\) −19.3485 + 11.1708i −0.836507 + 0.482958i
\(536\) −8.84847 5.10867i −0.382196 0.220661i
\(537\) 0 0
\(538\) 10.2247 17.7098i 0.440820 0.763523i
\(539\) 3.11416i 0.134136i
\(540\) 0 0
\(541\) −15.1742 + 26.2825i −0.652391 + 1.12997i 0.330150 + 0.943929i \(0.392901\pi\)
−0.982541 + 0.186046i \(0.940433\pi\)
\(542\) −15.6969 + 27.1879i −0.674241 + 1.16782i
\(543\) 0 0
\(544\) 2.04989i 0.0878882i
\(545\) 12.0000 20.7846i 0.514024 0.890315i
\(546\) 0 0
\(547\) −1.80306 1.04100i −0.0770933 0.0445099i 0.460958 0.887422i \(-0.347506\pi\)
−0.538051 + 0.842912i \(0.680839\pi\)
\(548\) 5.44949 3.14626i 0.232791 0.134402i
\(549\) 0 0
\(550\) 1.90702i 0.0813158i
\(551\) 1.22474 10.6066i 0.0521759 0.451856i
\(552\) 0 0
\(553\) 1.19694 0.691053i 0.0508990 0.0293866i
\(554\) −4.55051 7.88171i −0.193333 0.334862i
\(555\) 0 0
\(556\) 3.50000 + 6.06218i 0.148433 + 0.257094i
\(557\) 22.5959 + 13.0458i 0.957420 + 0.552767i 0.895378 0.445307i \(-0.146905\pi\)
0.0620418 + 0.998074i \(0.480239\pi\)
\(558\) 0 0
\(559\) 23.2952i 0.985282i
\(560\) 1.77526 + 1.02494i 0.0750182 + 0.0433118i
\(561\) 0 0
\(562\) 23.1464 0.976373
\(563\) −25.5959 −1.07874 −0.539370 0.842069i \(-0.681337\pi\)
−0.539370 + 0.842069i \(0.681337\pi\)
\(564\) 0 0
\(565\) 21.0000 12.1244i 0.883477 0.510075i
\(566\) 7.44949 12.9029i 0.313125 0.542349i
\(567\) 0 0
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) 31.1010 1.30382 0.651911 0.758295i \(-0.273967\pi\)
0.651911 + 0.758295i \(0.273967\pi\)
\(570\) 0 0
\(571\) −3.69694 −0.154712 −0.0773560 0.997004i \(-0.524648\pi\)
−0.0773560 + 0.997004i \(0.524648\pi\)
\(572\) 1.89898 + 3.28913i 0.0794003 + 0.137525i
\(573\) 0 0
\(574\) 0 0
\(575\) −14.6969 + 8.48528i −0.612905 + 0.353861i
\(576\) 0 0
\(577\) 5.79796 0.241372 0.120686 0.992691i \(-0.461491\pi\)
0.120686 + 0.992691i \(0.461491\pi\)
\(578\) 12.7980 0.532325
\(579\) 0 0
\(580\) −3.00000 1.73205i −0.124568 0.0719195i
\(581\) 17.1134i 0.709985i
\(582\) 0 0
\(583\) 2.69694 + 1.55708i 0.111696 + 0.0644876i
\(584\) 1.05051 + 1.81954i 0.0434704 + 0.0752930i
\(585\) 0 0
\(586\) 5.32577 + 9.22450i 0.220005 + 0.381060i
\(587\) 24.1237 13.9278i 0.995693 0.574863i 0.0887216 0.996056i \(-0.471722\pi\)
0.906971 + 0.421193i \(0.138389\pi\)
\(588\) 0 0
\(589\) −1.65153 3.81405i −0.0680501 0.157155i
\(590\) 20.4347i 0.841282i
\(591\) 0 0
\(592\) −2.17423 + 1.25529i −0.0893605 + 0.0515923i
\(593\) −13.4722 7.77817i −0.553237 0.319411i 0.197190 0.980365i \(-0.436818\pi\)
−0.750426 + 0.660954i \(0.770152\pi\)
\(594\) 0 0
\(595\) −2.10102 + 3.63907i −0.0861334 + 0.149188i
\(596\) 20.1489i 0.825333i
\(597\) 0 0
\(598\) 16.8990 29.2699i 0.691051 1.19693i
\(599\) 18.7980 32.5590i 0.768064 1.33033i −0.170548 0.985349i \(-0.554554\pi\)
0.938611 0.344976i \(-0.112113\pi\)
\(600\) 0 0
\(601\) 10.2173i 0.416774i −0.978046 0.208387i \(-0.933179\pi\)
0.978046 0.208387i \(-0.0668213\pi\)
\(602\) −2.82577 + 4.89437i −0.115170 + 0.199480i
\(603\) 0 0
\(604\) 1.34847 + 0.778539i 0.0548684 + 0.0316783i
\(605\) −12.9773 + 7.49245i −0.527602 + 0.304611i
\(606\) 0 0
\(607\) 2.16064i 0.0876979i −0.999038 0.0438489i \(-0.986038\pi\)
0.999038 0.0438489i \(-0.0139620\pi\)
\(608\) −0.500000 + 4.33013i −0.0202777 + 0.175610i
\(609\) 0 0
\(610\) 4.22474 2.43916i 0.171055 0.0987586i
\(611\) −6.12372 10.6066i −0.247739 0.429097i
\(612\) 0 0
\(613\) −9.44949 16.3670i −0.381661 0.661057i 0.609639 0.792680i \(-0.291315\pi\)
−0.991300 + 0.131623i \(0.957981\pi\)
\(614\) 13.3485 + 7.70674i 0.538700 + 0.311019i
\(615\) 0 0
\(616\) 0.921404i 0.0371244i
\(617\) −28.1010 16.2241i −1.13130 0.653159i −0.187042 0.982352i \(-0.559890\pi\)
−0.944263 + 0.329193i \(0.893223\pi\)
\(618\) 0 0
\(619\) −36.3939 −1.46279 −0.731397 0.681952i \(-0.761131\pi\)
−0.731397 + 0.681952i \(0.761131\pi\)
\(620\) −1.34847 −0.0541558
\(621\) 0 0
\(622\) 4.47219 2.58202i 0.179319 0.103530i
\(623\) −8.87628 + 15.3742i −0.355620 + 0.615953i
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) 22.6969 0.907152
\(627\) 0 0
\(628\) 12.3485 0.492758
\(629\) −2.57321 4.45694i −0.102601 0.177710i
\(630\) 0 0
\(631\) −7.27526 + 12.6011i −0.289623 + 0.501642i −0.973720 0.227749i \(-0.926863\pi\)
0.684096 + 0.729392i \(0.260197\pi\)
\(632\) 0.825765 0.476756i 0.0328472 0.0189643i
\(633\) 0 0
\(634\) −7.34847 −0.291845
\(635\) −12.0000 −0.476205
\(636\) 0 0
\(637\) −25.3485 14.6349i −1.00434 0.579858i
\(638\) 1.55708i 0.0616453i
\(639\) 0 0
\(640\) 1.22474 + 0.707107i 0.0484123 + 0.0279508i
\(641\) 23.0227 + 39.8765i 0.909342 + 1.57503i 0.814980 + 0.579489i \(0.196748\pi\)
0.0943619 + 0.995538i \(0.469919\pi\)
\(642\) 0 0
\(643\) −21.2980 36.8891i −0.839910 1.45477i −0.889970 0.456020i \(-0.849275\pi\)
0.0500601 0.998746i \(-0.484059\pi\)
\(644\) −7.10102 + 4.09978i −0.279819 + 0.161554i
\(645\) 0 0
\(646\) −8.87628 1.02494i −0.349232 0.0403259i
\(647\) 2.97129i 0.116814i −0.998293 0.0584068i \(-0.981398\pi\)
0.998293 0.0584068i \(-0.0186020\pi\)
\(648\) 0 0
\(649\) 7.95459 4.59259i 0.312245 0.180275i
\(650\) 15.5227 + 8.96204i 0.608851 + 0.351520i
\(651\) 0 0
\(652\) −3.84847 + 6.66574i −0.150718 + 0.261051i
\(653\) 38.3908i 1.50235i −0.660103 0.751175i \(-0.729487\pi\)
0.660103 0.751175i \(-0.270513\pi\)
\(654\) 0 0
\(655\) −10.4495 + 18.0990i −0.408295 + 0.707188i
\(656\) 0 0
\(657\) 0 0
\(658\) 2.97129i 0.115833i
\(659\) 5.69694 9.86739i 0.221921 0.384379i −0.733470 0.679722i \(-0.762101\pi\)
0.955391 + 0.295343i \(0.0954339\pi\)
\(660\) 0 0
\(661\) −23.6969 13.6814i −0.921704 0.532146i −0.0375258 0.999296i \(-0.511948\pi\)
−0.884178 + 0.467150i \(0.845281\pi\)
\(662\) −16.1969 + 9.35131i −0.629512 + 0.363449i
\(663\) 0 0
\(664\) 11.8065i 0.458182i
\(665\) −5.32577 + 7.17461i −0.206524 + 0.278219i
\(666\) 0 0
\(667\) 12.0000 6.92820i 0.464642 0.268261i
\(668\) 4.22474 + 7.31747i 0.163460 + 0.283122i
\(669\) 0 0
\(670\) −7.22474 12.5136i −0.279116 0.483444i
\(671\) −1.89898 1.09638i −0.0733093 0.0423251i
\(672\) 0 0
\(673\) 19.0526i 0.734422i 0.930138 + 0.367211i \(0.119687\pi\)
−0.930138 + 0.367211i \(0.880313\pi\)
\(674\) −1.80306 1.04100i −0.0694513 0.0400977i
\(675\) 0 0
\(676\) −22.6969 −0.872959
\(677\) 37.3485 1.43542 0.717709 0.696343i \(-0.245191\pi\)
0.717709 + 0.696343i \(0.245191\pi\)
\(678\) 0 0
\(679\) −23.6969 + 13.6814i −0.909405 + 0.525045i
\(680\) −1.44949 + 2.51059i −0.0555854 + 0.0962767i
\(681\) 0 0
\(682\) 0.303062 + 0.524918i 0.0116048 + 0.0201001i
\(683\) −28.0454 −1.07313 −0.536564 0.843860i \(-0.680278\pi\)
−0.536564 + 0.843860i \(0.680278\pi\)
\(684\) 0 0
\(685\) 8.89898 0.340013
\(686\) 8.62372 + 14.9367i 0.329255 + 0.570287i
\(687\) 0 0
\(688\) −1.94949 + 3.37662i −0.0743236 + 0.128732i
\(689\) −25.3485 + 14.6349i −0.965700 + 0.557547i
\(690\) 0 0
\(691\) −0.696938 −0.0265128 −0.0132564 0.999912i \(-0.504220\pi\)
−0.0132564 + 0.999912i \(0.504220\pi\)
\(692\) 12.2474 0.465578
\(693\) 0 0
\(694\) 28.2247 + 16.2956i 1.07140 + 0.618571i
\(695\) 9.89949i 0.375509i
\(696\) 0 0
\(697\) 0 0
\(698\) −11.6237 20.1329i −0.439964 0.762041i
\(699\) 0 0
\(700\) −2.17423 3.76588i −0.0821783 0.142337i
\(701\) 13.4722 7.77817i 0.508838 0.293778i −0.223518 0.974700i \(-0.571754\pi\)
0.732356 + 0.680922i \(0.238421\pi\)
\(702\) 0 0
\(703\) −4.34847 10.0424i −0.164006 0.378755i
\(704\) 0.635674i 0.0239579i
\(705\) 0 0
\(706\) −2.87628 + 1.66062i −0.108250 + 0.0624982i
\(707\) −16.5959 9.58166i −0.624154 0.360355i
\(708\) 0 0
\(709\) −3.17423 + 5.49794i −0.119211 + 0.206479i −0.919455 0.393195i \(-0.871370\pi\)
0.800244 + 0.599674i \(0.204703\pi\)
\(710\) 8.48528i 0.318447i
\(711\) 0 0
\(712\) −6.12372 + 10.6066i −0.229496 + 0.397499i
\(713\) 2.69694 4.67123i 0.101001 0.174939i
\(714\) 0 0
\(715\) 5.37113i 0.200869i
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) −9.79796 5.65685i −0.365657 0.211112i
\(719\) 17.1464 9.89949i 0.639454 0.369189i −0.144950 0.989439i \(-0.546302\pi\)
0.784404 + 0.620250i \(0.212969\pi\)
\(720\) 0 0
\(721\) 20.9596i 0.780576i
\(722\) −18.5000 4.33013i −0.688499 0.161151i
\(723\) 0 0
\(724\) 4.65153 2.68556i 0.172873 0.0998081i
\(725\) 3.67423 + 6.36396i 0.136458 + 0.236352i
\(726\) 0 0
\(727\) −4.82577 8.35847i −0.178978 0.309999i 0.762553 0.646926i \(-0.223946\pi\)
−0.941531 + 0.336927i \(0.890612\pi\)
\(728\) 7.50000 + 4.33013i 0.277968 + 0.160485i
\(729\) 0 0
\(730\) 2.97129i 0.109972i
\(731\) −6.92168 3.99624i −0.256008 0.147806i
\(732\) 0 0
\(733\) −30.6969 −1.13382 −0.566909 0.823781i \(-0.691861\pi\)
−0.566909 + 0.823781i \(0.691861\pi\)
\(734\) −14.3485 −0.529612
\(735\) 0 0
\(736\) −4.89898 + 2.82843i −0.180579 + 0.104257i
\(737\) −3.24745 + 5.62475i −0.119621 + 0.207190i
\(738\) 0 0
\(739\) −23.1969 40.1783i −0.853313 1.47798i −0.878201 0.478292i \(-0.841256\pi\)
0.0248879 0.999690i \(-0.492077\pi\)
\(740\) −3.55051 −0.130519
\(741\) 0 0
\(742\) 7.10102 0.260687
\(743\) −23.6969 41.0443i −0.869356 1.50577i −0.862656 0.505792i \(-0.831200\pi\)
−0.00670079 0.999978i \(-0.502133\pi\)
\(744\) 0 0
\(745\) −14.2474 + 24.6773i −0.521986 + 0.904107i
\(746\) −10.6515 + 6.14966i −0.389980 + 0.225155i
\(747\) 0 0
\(748\) 1.30306 0.0476446
\(749\) 22.8990 0.836711
\(750\) 0 0
\(751\) 24.2196 + 13.9832i 0.883787 + 0.510255i 0.871905 0.489675i \(-0.162884\pi\)
0.0118820 + 0.999929i \(0.496218\pi\)
\(752\) 2.04989i 0.0747517i
\(753\) 0 0
\(754\) −12.6742 7.31747i −0.461568 0.266487i
\(755\) 1.10102 + 1.90702i 0.0400702 + 0.0694037i
\(756\) 0 0
\(757\) −12.1742 21.0864i −0.442480 0.766398i 0.555393 0.831588i \(-0.312568\pi\)
−0.997873 + 0.0651902i \(0.979235\pi\)
\(758\) 16.5000 9.52628i 0.599307 0.346010i
\(759\) 0 0
\(760\) −3.67423 + 4.94975i −0.133278 + 0.179546i
\(761\) 44.8262i 1.62495i 0.582996 + 0.812475i \(0.301880\pi\)
−0.582996 + 0.812475i \(0.698120\pi\)
\(762\) 0 0
\(763\) −21.3031 + 12.2993i −0.771223 + 0.445266i
\(764\) 13.2247 + 7.63531i 0.478454 + 0.276236i
\(765\) 0 0
\(766\) −5.44949 + 9.43879i −0.196898 + 0.341037i
\(767\) 86.3312i 3.11724i
\(768\) 0 0
\(769\) 1.29796 2.24813i 0.0468056 0.0810697i −0.841673 0.539987i \(-0.818429\pi\)
0.888479 + 0.458917i \(0.151763\pi\)
\(770\) 0.651531 1.12848i 0.0234795 0.0406678i
\(771\) 0 0
\(772\) 17.1455i 0.617081i
\(773\) 4.47219 7.74607i 0.160854 0.278607i −0.774321 0.632792i \(-0.781909\pi\)
0.935175 + 0.354186i \(0.115242\pi\)
\(774\) 0 0
\(775\) 2.47730 + 1.43027i 0.0889871 + 0.0513767i
\(776\) −16.3485 + 9.43879i −0.586876 + 0.338833i
\(777\) 0 0
\(778\) 26.4415i 0.947972i
\(779\) 0 0
\(780\) 0 0
\(781\) 3.30306 1.90702i 0.118193 0.0682387i
\(782\) −5.79796 10.0424i −0.207335 0.359114i
\(783\) 0 0
\(784\) 2.44949 + 4.24264i 0.0874818 + 0.151523i
\(785\) 15.1237 + 8.73169i 0.539789 + 0.311647i
\(786\) 0 0
\(787\) 24.0737i 0.858136i 0.903272 + 0.429068i \(0.141158\pi\)
−0.903272 + 0.429068i \(0.858842\pi\)
\(788\) 17.5732 + 10.1459i 0.626020 + 0.361433i
\(789\) 0 0